engShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2018-09-016111210.22044/jas.2017.6012.13011251MAXIMAL PRYM VARIETY AND MAXIMAL MORPHISMM. Farhadi Sangdehifarhadi@du.ac.ir1departement of math and computer science Damghan UniversityWe investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized <br /> definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.http://jas.shahroodut.ac.ir/article_1251_754f567f47608f98c2a43186b7dde0ee.pdfPrym VarietyMaximal CurveMaximal MorphismengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2018-09-0161132810.22044/jas.2017.5482.12781252SIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIALE. Ghasemiane.ghasemian@yahoo.com1Gh. H. Fath-Tabarfathtabar@kashanu.ac.ir2Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran.Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran.Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to<br /> {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefﬁcients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.http://jas.shahroodut.ac.ir/article_1252_6c32e6bd4ccfe3ab6aa2450e8fa4c181.pdfSinged graphSigned Petersen graphAdjacency matrixSigned Laplacian matrixengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2018-09-0161294210.22044/jas.2018.5530.12801253IDEALS WITH (d1, . . . , dm)-LINEAR QUOTIENTSL. Sharifanleilasharifan@gmail.com1Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran and School of Mathematics, Institute for research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran.In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.http://jas.shahroodut.ac.ir/article_1253_6f8ef72f643795159174715408d317ee.pdfMapping conecomponentwise linear moduleregularityengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2018-09-0161435710.22044/jas.2018.6259.13111254ON MAXIMAL IDEALS OF R∞LA. A. Estajiaaestaji@gmail.com1A. Mahmoudi Darghadamm.darghadam@yahoo.com2Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. Email: aaestaji@hsu.ac.ir and aaestaji@gmail.comFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. Email: m.darghadam@yahoo.comLet $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions<br /> on $L$.<br /> We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n})<br /> mbox{ is a compact frame for any $n in mathbb{N}$}}.$$<br /> Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the<br /> set ${x in X: |f(x)|geq dfrac{1}{n} }$<br /> is compact, for every $n in mathbb{N}$.<br /> Kohls has shown that $C_{infty} (X)$ is precisely the intersection<br /> of all the free maximal ideals of $C^{*}(X)$.<br /> The aim of this paper is to<br /> extend this result to<br /> the real continuous functions on a<br /> frame and hence we show that $mathcal{R}_{infty}L$ is precisely the intersection<br /> of all the free maximal ideals of $mathcal R^{*}L$.<br /> This result is used to characterize the maximal ideals in $mathcal{R}_{infty}L$.http://jas.shahroodut.ac.ir/article_1254_45a4703f3fc3297b882c27efeed5d7db.pdfFrameCompactMaximal idealRing of real valued continuous functionsengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2018-09-0161597010.22044/jas.2018.5360.12731255THE LATTICE OF CONGRUENCES ON A TERNARY SEMIGROUPN. Ashrafinashrafi@semnan.ac.ir1Z. Yazdanmehrzhyazdanmehr@gmail.com2Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: nashrafi@semnan.ac.irFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: zhyazdanmehr@gmail.comIn this paper we investigate some properties of congruences on ternary semigroups. We also deﬁne the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular, it is not even semimodular. Then we indicate some conditions under which this lattice is modular.http://jas.shahroodut.ac.ir/article_1255_585b8d0ca4e05982b434b1a9d2ab912e.pdfTernary semigroupcongruenceLatticeengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2018-09-0161718010.22044/jas.2018.6328.13161256ON THE CHARACTERISTIC DEGREE OF FINITE GROUPSZ. Sepehrizadehzohreh.sepehri@gmail.com1M. R. Rismanchianrismanchian133@gmail.com2Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: zohreh.sepehri@gmail.comDepartment of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: rismanchian133@gmail.com, rismanchian@sku.ac.irIn this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic in G. We determine the upper and lower bounds for this probability. We also obtain a special lower bound, when H is a cyclic p-subgroup of G.http://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdfAutocommutativity degreeCharacteristic degreep-group